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%I #19 Jul 08 2023 16:02:40
%S 5,5577,6435661,7426747025,8570459630997,9890302987423321,
%T 11413401077026881245,13171054952586033533217,
%U 15199386001883205670450981,17540078275118266757666898665,20241235130100477955141930608237,23358367800057676441967030255006641
%N Numbers k such that 6k^2-2k = 3n^2-n for some integer n>0.
%C Also indices of pentagonal numbers which are half of some other pentagonal number: see A137693 for more details, comments and links.
%H Colin Barker, <a href="/A137694/b137694.txt">Table of n, a(n) for n = 1..250</a>
%H Dario Alpern, <a href="https://www.alpertron.com.ar/QUAD.HTM">Quadratic two integer variable equation solver</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1155,-1155,1).
%F a(n) = f^{2n-2}(5,7)[1], where f(x,y) = (577x + 408y - 164, 816x + 577y - 232).
%F a(n) = (5,7,1,5,7,1,...) (mod 10).
%F G.f.: -x*(5-198*x+x^2) / ( (x-1)*(x^2-1154*x+1) ). - _R. J. Mathar_, Apr 17 2011
%o (PARI) vector(20,i, (v=if(i>1,[577,408;816,577]*v-[164;232], [5;7]))[1,1])
%Y Cf. A000326, A136112-A136118, A135768-A135769, A137693.
%K easy,nonn
%O 1,1
%A _M. F. Hasler_, Feb 08 2008
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